Certain computational problems, such as the factoring of large numbers, cannot easily be solved using conventional computers due to the time required to complete the computation. It has, however, been shown that quantum computers can use non-classical algorithmic methods to provide efficient solutions to certain of these types of computational problems.
The fundamental unit of quantum information in a quantum computer is called a quantum bit, or qubit. Quantum computers can use a binary representation of numbers, just as conventional binary computers. In addition, quantum systems can also make us of use multi-valued logic and data, in which case, the atomic quantum datum is referred to as a “qudit”. An individual qubit or qudit datum can be physically represented by the state of a quantum system. However, in a quantum system, the datum can be considered to be in more than one of the possible states at any single given time. Thus, in the case of a qubit, the datum can be in a state that represents both a zero and a one at the same time. This state is referred to as superposition. Quantum superpositions of this kind are fundamentally different from classical data representations, even when classical probabilities are taken into account. It is only when a quantum datum is observed that its value “collapses” into a well-defined, single state. This “collapse” is referred to as decoherence.
Thus, while bits in the classical computing model always have a well-defined value (e.g., 0 or 1), qubits in superposition have some simultaneous probability of being in both of the two states representing 0 and 1. It is customary to represent the general state of a quantum system by |ψ>, and let |0> and |1> represent the quantum states corresponding to the values 0 and 1, respectively. Quantum mechanics allows superpositions of these two states, given by|ψ>=α|0>+β|1>where α and β are complex numbers. In this case, the probability of observing the system in the state |0> is equal to α2 the probability of the state |1> is β2.
Quantum computers may utilize physical particles to represent or implement these qubits or qudits. One example is the spin of an electron, wherein the up or down spin can correspond to a 0, a 1, or a superposition of states in which it is both up and down at the same time. Performing a calculation using the electron may essentially perform the operation simultaneously for both a 0 and a 1. Similarly, in the photonic approach to quantum computing, a “0” may be represented by the possibility of observing a single photon in a given path, whereas the potential for observing the same photon in a different path may represent a “1”.
For example, consider a single photon passing through an interferometer with two paths, with phase shifts φ1 and φ2 inserted in the two paths respectively. A beam splitter gives a 50% probability that the photon will travel in one path or the other. If a measurement is made to determine where the photon is located, it will be found in only one of the two paths. But if no such measurement is made, a single photon can somehow experience both phase shifts φ1 and φ2 simultaneously. This suggests that in some sense a photon must be located in both paths simultaneously if no measurement is made to determine its position. This effect can be experimentally verified by observing the interference pattern resulting from the interaction of the two paths when only a single photon is allowed to transit through the apparatus at a given time. Of course, if there are more than a single pair of possible photonic paths, then the resulting system can be said to represent a qudit.
One of the most challenging problems with practical quantum computing, however, is the realization of the physical system that represents the qubits themselves. More specifically, the scale at which qubits are typically implemented (e.g., a single electron, a single photon, etc.) means that any perturbations in the qubit caused by unwanted interactions with the environment (e.g., temperature, magnetic field, etc.) may result in an alteration to the state of the qubit or even decoherence. Quantum coherence preservation (e.g., maintenance or storage of the qubit in a quantum state for any useful time period) within a single qubit (or multiple qubits) is thus a major obstacle to the useful implementation of quantum computing. Exacerbating the problem is the fact that when several such qubits are placed in close proximity to one another they can potentially mutually interfere (e.g., electromagnetically) with each other and, thereby, affect adjacent qubits. In some cases, that interference is desired (in the case of quantum data computation operations, for example), but in the case where that interference is uncontrolled, then it can lead to incorrect computational results. Such unwanted interference effects are sometimes referred to as quantum gate or processing infidelities.
Accordingly, there is a need to for systems and methods that can both preserve coherence of a qubit from external interference as well as to allow the operations on that qubit to be corrected in the presence of unwanted quantum operational infidelities.